Jarzynski equation for a simple quantum system: Comparing two definitions of work

The validity of the Jarzynski equation for a very simple, exactly solvable quantum system is analyzed. The implications of two different definitions of work proposed in the literature are investigated. The first one derives from measurements of the system energy at the beginning and at the end of the process under consideration making the work a classical stochastic variable with transition probabilities derived from quantum mechanics. In the second definition an operator of work is introduced and the average in the Jarzynski equation is a quantum expectation value. For the first definition a general quantum mechanical version of the Jarzynski equation is known to hold. For the second one the Jarzynski equation fails to yield the free energy difference at low temperature.Comment: 5 papes, 1 figure largly rewritten and slightly enlarged versio

Recombining your way out of trouble: the genetic architecture of hybrid fitness under environmental stress

Hybridization between species is a fundamental evolutionary force that can both promote and delay adaptation. There is a deficit in our understanding of the genetic basis of hybrid fitness, especially in non-domesticated organisms. We also know little about how hybrid fitness changes as a function of environmental stress. Here, we made genetically variable F2 hybrid populations from two divergent Saccharomyces yeast species, exposed populations to ten toxins, and sequenced the most resilient hybrids on low coverage using ddRADseq. We expected to find strong negative epistasis and heterozygote advantage in the hybrid genomes. We investigated three aspects of hybridness: 1) hybridity, 2) interspecific heterozygosity, and 3) epistasis (positive or negative associations between non-homologous chromosomes). Linear mixed effect models revealed strong genotype-by-environment interactions with many chromosomes and chromosomal interactions showing species-biased content depending on the environment. Against our predictions, we found extensive selection against heterozygosity such that homozygous allelic combinations from the same species were strongly overrepresented in an otherwise hybrid genomic background. We also observed multiple cases of positive epistasis between chromosomes from opposite species, confirmed by epistasis- and selection-free simulations, which is surprising given the large divergence of the parental species (~15% genome-wide). Together, these results suggest that stress-resilient hybrid genomes can be assembled from the best features of both parents, without paying high costs of negative epistasis across large evolutionary distances. Our findings illustrate the importance of measuring genetic trait architecture in an environmental context when determining the evolutionary potential of hybrid populations

Soliton excitation in waveguide arrays with an effective intermediate dimensionality

We reveal and observe experimentally significant modifications undertaken by discrete solitons in waveguide lattices upon the continuous transformation of the lattice structure from one-dimensional to two-dimensional. Light evolution and soliton excitation in arrays with a gradually increasing number of rows are investigated, yielding solitons with an effective reduced dimensionality residing at the edge and in the bulk of the lattice.Comment: 14 pages, 5 figures, to appear in Physical Review Letter

Hybrid Bloch-Anderson localization of light

We investigate the interplay of Bloch oscillations and Anderson localization in optics. Gradual washing out of Bloch oscillations and the formation of nearly stationary averaged intensity distributions, which are symmetric for narrow and strongly asymmetric for broad input excitations, are observed experimentally in laser-written waveguide arrays. At large disorder levels Bloch oscillations are completely destroyed and both narrow and wide excitations lead to symmetric stationary averaged intensity distributions with exponentially decaying tails.Comment: 3 pages, 6 figures, to appear in Optics Letter

Prototype-based analysis of GAMA galaxy catalogue data

We present a prototype-based machine learning analysis of labeled galaxy catalogue data containing parameters from the Galaxy and Mass Assembly (GAMA) survey. Using both an unsupervised and supervised method, the Self-Organizing Map and Generalized Relevance Matrix Learning Vec- tor Quantization, we find that the data does not fully support the popular visual-inspection-based galaxy classification scheme employed to categorize the galaxies. In particular, only one class, the Little Blue Spheroids, is consistently separable from the other classes. In a proof-of-concept experiment, we present the galaxy parameters that are most discriminative for this class

3D shape reconstruction of the femur from planar X-ray images using statistical shape and appearance models

Major trauma is a condition that can result in severe bone damage. Customised orthopaedic reconstruction allows for limb salvage surgery and helps to restore joint alignment. For the best possible outcome three dimensional (3D) medical imaging is necessary, but its availability and access, especially in developing countries, can be challenging. In this study, 3D bone shapes of the femur reconstructed from planar radiographs representing bone defects were evaluated for use in orthopaedic surgery. Statistical shape and appearance models generated from 40 cadaveric X-ray computed tomography (CT) images were used to reconstruct 3D bone shapes. The reconstruction simulated bone defects of between 0% and 50% of the whole bone, and the prediction accuracy using anterior–posterior (AP) and anterior–posterior/medial–lateral (AP/ML) X-rays were compared. As error metrics for the comparison, measures evaluating the distance between contour lines of the projections as well as a measure comparing similarities in image intensities were used. The results were evaluated using the root-mean-square distance for surface error as well as differences in commonly used anatomical measures, including bow, femoral neck, diaphyseal–condylar and version angles between reconstructed surfaces from the shape model and the intact shape reconstructed from the CT image. The reconstructions had average surface errors between 1.59 and 3.59 mm with reconstructions using the contour error metric from the AP/ML directions being the most accurate. Predictions of bow and femoral neck angles were well below the clinical threshold accuracy of 3°, diaphyseal–condylar angles were around the threshold of 3° and only version angle predictions of between 5.3° and 9.3° were above the clinical threshold, but below the range reported in clinical practice using computer navigation (i.e., 17° internal to 15° external rotation). This study shows that the reconstructions from partly available planar images using statistical shape and appearance models had an accuracy which would support their potential use in orthopaedic reconstruction

Particle alignments and shape change in 66^{66}Ge and 68^{68}Ge

The structure of the $N \approx Z$ nuclei $^{66}$Ge and $^{68}$Ge is studied by the shell model on a spherical basis. The calculations with an extended $P+QQ$ Hamiltonian in the configuration space ($2p_{3/2}$, $1f_{5/2}$, $2p_{1/2}$, $1g_{9/2}$) succeed in reproducing experimental energy levels, moments of inertia and $Q$ moments in Ge isotopes. Using the reliable wave functions, this paper investigates particle alignments and nuclear shapes in $^{66}$Ge and $^{68}$Ge. It is shown that structural changes in the four sequences of the positive- and negative-parity yrast states with even $J$ and odd $J$ are caused by various types of particle alignments in the $g_{9/2}$ orbit. The nuclear shape is investigated by calculating spectroscopic $Q$ moments of the first and second $2^+$ states, and moreover the triaxiality is examined by the constrained Hatree-Fock method. The changes of the first band crossing and the nuclear deformation depending on the neutron number are discussed.Comment: 18 pages, 21 figures; submitted to Phys. Rev.